# Module Information

Module Identifier
MA37210
Module Title
Time Series Analysis
Academic Year
2013/2014
Co-ordinator
Semester
Semester 1
Mutually Exclusive
Pre-Requisite
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 18 x 1 hour
Seminars / Tutorials 4 x 1 hour
Workload Breakdown (Every 10 credits carries a notional student workload of 100 hours.) Lectures and tutorials 22 hours Worksheets (4x5 hours) 20 hours Private study 56 hours Formal examination 2 hours

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   conventional examination  100%

### Learning Outcomes

On completion of this module, students should be able to:
1. understand the ideas of autocorrelation;

2. calculate autocovariances and autocorrelations for linear time series models;

3. identify suitable models for different data sets;

4. use models to forecast future values and set confidence limits on them.

### Aims

To introduce students to the vast area of Time Series Analysis and Forecasting as a branch of statistical methodology.

### Brief description

Time Series Analysis has, over the past 30 years, been one of the fastest growing areas of Statistics. It is concerned with situations where data or random variables are generated sequentially through time, and this makes the variables involved dependent on one another as opposed to having independent variables as in most other Statistics problems. This module develops a class of models to cater for such dependence, and considers how they are fitted to data, as well as how they may be used to forecast future values beyond the data set.

### Content

Introduction
Historical background; theoretical properties of time series; the ideas of stationarity and invertibility; backward shift and difference operators
Linear Time Series Models
General linear filters. Autoregressive, Moving Average and mixed models. The ARMA family. Techniques for evaluating autocorrelation and partial autocorrelation functions. Aggregation and the case for ARMA models. Non-stationarity and ARIMA models.
Model Fitting
Identification, estimation and diagnostic checking as an iterative process. Sample autocorrelations. Least squares and conditional least squares. Differencing to achieve stationarity.
Forecasting
Minimum mean squared error. The Fundamental Theorem of Forecasting. Forecast error variances.

### Module Skills

Skills Type Skills details
Application of Number Throughout the module
Communication Written worksheet solutions.
Improving own Learning and Performance Feedback via tutorials
Information Technology Interpretation of specialist computer output.
Personal Development and Career planning Students exposed to an area of Statistics that has wide applicability.
Problem solving Problem solving is central to the development of time series models, and to the ultimate goal of producing accurate forecasts of future values.
Research skills Students encouraged to consult relevant literature and compare various methods.
Subject Specific Skills General modeling ability.
Team work N/A

### Reading List

Recommended Text
Chatfield, Christopher. (c2003.) The analysis of time series :an introduction /Chris Chatfield. http://www.loc.gov/catdir/enhancements/fy0646/2003051472-d.html 6th ed. Chapman &amp;amp; Hall/CRC Cryer, Jonathan D. (c2008.) Time series analysis :with applications in R /Jonathan D. Cryer, Kung-Sik Chan. http://www.loc.gov/catdir/toc/fy0804/2008923058.html 2nd ed. Springer Kendall, Maurice G. (1990.) Time-series /Sir Maurice Kendall and J. Keith Ord. 3rd ed E.Arnold Primo search Wei, William W. S. (1989.) Time series analysis :univariate and multivariate methods /William W.S. Wei. Addison-Wesley Primo search
Supplementary Text
Box, George E. P. (c2008.) Time series analysis :forecasting and control /George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel. 4th ed. John Wiley Primo search

### Notes

This module is at CQFW Level 6